Question: Rewrite as a simplified fraction. ${1.42\overline{4} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1424.4444...\\ 100x &= 142.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1282}$ ${x = \dfrac{1282}{900}} $ ${x = \dfrac{641}{450}} \text{or} {1 \dfrac{191}{450}}$